Influence of external periodic and non-linear factors upon stability of economic systems

The article conducts a study of influence of periodic effect upon economic systems. It shows a danger of the resonance case when frequency of external periodic effect on the system tends to its own frequency of vibrations near the state of equilibrium. In this case, the amplitude of vibrations of the system becomes proportional to time and grows with it. Account of impacts, proportional to the rate of shift from the state of equilibrium, results in limitation of growth of the amplitude of vibrations, taking away secular dependence. Account of actions, proportional to non-linear shifts from the point of equilibrium, points out a possibility of taking the system out of the resonance. Quadratic non-linearity has no influence upon changes of the amplitude and vibration phase and cubic non-linearity changes the vibration phase through the amplitude, which takes the system out of the resonance. Depending on the system parameters, the case of a sudden change of the amplitude during the change of difference between the own frequency of the system and frequency of periodic effect is possible, moreover, the system passes to a stable state. The article offers methods of treating monitoring data for qualitative analysis of dynamics of economic systems.